dMafart_model {bioinactivation} | R Documentation |

## First Derivate of the Weibull-Mafart Model

### Description

Calculates the first derivative of Weibull-Mafart model at a given time for the model parameters provided and the environmental conditions given.

### Usage

```
dMafart_model(t, x, parms, temp_profile)
```

### Arguments

`t` |
numeric vector indicating the time of the experiment. |

`x` |
list with the value of N at t. |

`parms` |
parameters for the secondary model. No explicit check of their validity
is performed (see section |

`temp_profile` |
a function that provides the temperature at a given time. |

### Details

The model is developed from the isothermal Weibull-Mafart model without
taking into
account in the derivation the time dependence of `\delta_T`

for
non-isothermal temperature profiles.

This function is compatible with the function
`predict_inactivation`

.

### Value

The value of the first derivative of N at time `t`

as a list.

### Model Equation

`\frac{dN}{dt} = -N \cdot p \cdot (1/\delta)^p \cdot t^{p-1} `

`\delta(T) = \delta_{ref} \cdot 10^{- (T-T_ref)/z} `

### Model Parameters

temp_ref: Reference temperature for the calculation.

delta_ref: Value of the scale factor at the reference temperature.

z: z-value.

p: shape factor of the Weibull distribution.

### Note

For t=0, dN = 0 unless n=1. Hence, a small shift needs to be introduced to t.

### See Also

*bioinactivation*version 1.2.3 Index]